Numerical control systems for machine tools

ABSTRACT

In a numerical control system of a machine tool wherein a servo-system for driving tool, table etc. is controlled by a control instruction signal expressed by a given function equation, there are provided a control instruction signal generator which generates a signal representing a control instruction value, a correction device for producing a correction signal corresponding to a phase lag angle of a servo-drive system for driving a working shaft and a correction device for correcting the control instruction value in accordance with the correction signal.

BACKGROUND OF THE INVENTION

This invention relates to a numerical control system of a machine tooland, more particularly, to a control instruction value generating systemfor generating a control instruction value expressed by a complicatedfunction equation.

When numerically controlling a tool of a machine tool by simultaneouslycontrolling the position of the tool on the X and Y axes of rectangularcoordinates so as to move the tool along a predetermined locus on atable, the control instruction value given to the tool or tablecomprises a complicated function.

For example, when cutting or grinding a pin journal of the crankshaft ofan internal combustion engine to give it an outer contour of a truecircle, since the pin journal is located eccentrically with respect tothe main journal of the engine crankshaft, it is necessary to use aninstruction value expressed by a complicated function equation.

In the numerical control system of a machine tool, there is a problem ofoccurrence of a working error caused by time lag of the driving system(including the load) with respect to the instruction from the controldevice. For example, when both X and Y axes positions are simultaneouslycontrolled so as to move the tool along a curve on a plane, the phaselag caused by the inherent load characteristics of the servo-system ofthe machine tool, that is the resultant of the movements along X and Yaxes, has an influence upon the machining accuracy. Moreover, the effectcaused by the characteristics differs depending upon the rectangularcoordinates (xi, yi) of a working point. For this reason, according tothe prior art system it is difficult to work at high accuracies and itis necessary to use post machining. For example, for the purpose ofcutting or grinding of pin journal located eccentrically with respect tothe main journal of the crankshaft of an internal combustion engine togive it a true circular cross-section, when the axis of the pin journalis revolved about the axis of the main journal by holding it by a chuckand when a control system is used to cause a tool which rotates incontact with the periphery of the pin journal to linearly reciprocate tofollow said revolving motion, the time lag of a servo-system whichcauses linear motion of the tool head and the movement of the contactpoint (working point) between the workpiece and the tool are related ina complicated manner thus causing a working error.

SUMMARY OF THE INVENTION

It is an object of this invention to provide an improved numericalcontrol system of a machine tool capable of producing an accuratecontrol instruction from complicated function equation.

According to this invention, the control instruction function equationis decomposed into Fourier components, and these components areindependently calculated and then added together to generate a controlinstruction.

Another object of this invention is to provide an improved numericalcontrol system capable of machining with a minimum loss wherein thedriving instruction signal of a servo-system is precorrected by an erroranticipated by the inherent characteristic of the servo-system so as todrive the servo-system by the corrected instruction signal.

Still further object of this invention is to provide an accurate andefficient numerical control system of a machine tool wherein the controlinstruction signal and a feedback signal are intermittently comparedwith each other to intermittently calculate the control instruction.

According to this invention these and further objects can beaccomplished by providing a numerical control system of a machine toolwherein a servo-system for driving a tool, table, etc. of the machinetool is controlled by a control instruction signal expressed by apredetermined function equation, characterized by comprising a controlinstruction signal generator which generates a signal representing acontrol instruction value, a correction device for generating acorrection value corresponding to a phase lag angle of a servo-drivesystem for driving a working shaft of the machine tool and correctionmeans for correcting the control instruction value in accordance withthe correction signal.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 is a plan view showing one example of a machine tool to which theinvention is applicable;

FIG. 2 is a diagram showing the relationship between a grinding wheeland a pin journal to be machined;

FIG. 3 is a block diagram showing one example of the control systemembodying the invention;

FIGS. 4a and 4b show transfer functions utilized in the control systemshown in FIG. 3;

FIG. 5 is a block diagram showing another example of the tool postpositioning instruction function generator and of the correctionfunction generator;

FIG. 6 is a block diagram showing a modified correction device and

FIG. 7 is a block diagram showing one example of a control instructionvalue generating circuit.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to the accompanying drawings,

FIG. 1 is a plan view of a machine tool for grinding the pin journals 11(shaded portions) of a crankshaft 10 of an internal compustion engine.The main journal 12 of the crankshaft 10 is held by chucks 13 androtated by a work rotation control unit 14. Grinding wheels 15 aremounted on driving units 16 and driven by electric motors, not shown, inthe driving units. These driving units are reciprocated by servo-motors17 in the direction of Y axis and moved in the direction of X axis byshift motors 19 to vary the tool pitch.

FIG. 2 shows the positional relationship between one grinding wheel 15and one pin journal 11 to be ground which is rotated about point O₁ at aconstant angular velocity ω. As a consequence, the pin journal 11 isrevolved about the center O₁ with its same surface always being directedoutwardly. The grinding wheel 15 is rotated about point O₂ and it isnecessary to control the grinding wheel such that it is alwaysmaintained in contact with the outer periphery of the pin journal 11. Tothis end, it is necessary to displace the center O₂ of the grindingwheel 15 in accordance with the angular position (rotary angle θ) of theworkpiece 11. The displacement in the direction of Y axis is expressedas a function Y(t) of time (t) as shown by the following equation.

    Y(t)=E cos ωt+√(R+L).sup.2 -E.sup.2 sin.sup.2 ωt (1)

where ω represents the angular velocity of pin journal 11, that isω=dθ/dt, L the radius of the grinding wheel, R the radius of the pinjournal, and E the distance between the center of the pin journal 11 andits center of rotation O₁.

When the grinding wheel 15 moves just in accordance with the functionY(t) expressed by equation (1), the pin journal 11 would be exactlyground into a circle having radius R. The working path traced by thecontact point between the grinding wheel and the pin journal, that isthe working point is an annulus. Although the servo-motors 17 are drivenby using the function value Y(t) corresponding to the variation in therotary angle θ as an instruction value, due to the time delay in theresponse of the servo-system, a position error ε would result. Moreparticularly, the servo-system is driven in a direction to make zero thedifference between the present Y axis position Y_(o) (t) of the tooldriving unit 16 detected by a position detector and the instructionvalue Y(t) but there is a time delay before the difference is decreasedto zero. The position error ε caused by the time delay increases withthe angular speed ω but is solely determined to correspond to the rotaryangle θ so long as the angular velocity is constant.

FIG. 3 shows one example of the control device of this inventionprovided with a correction device that can substantially correct thetime delay. According to this correction device, the position error ε(t)is predetermined in accordance with the rotary angle θ, the instructionvalue Y(t) is corrected by the position error ε(t) and the resultingcorrected value Y(t)+ε(t) is used as a new instruction value for drivingthe servo system.

The correction device comprises a control unit for the workpiece drivingshaft 14 in which the rotation of an electric motor 22 is transmitted toa chuck 13 via a gear box 23 to rotate the workpiece 10. An angledetector 24 is provided to detect the rotary angle θ of the workpiece bydetecting the rotary angle of the chuck 13. A deviation signal between arotary angle instruction value θi from an external control and thepresent rotary angle θ is applied to motor 22 through a controlamplifier 25. The detected rotary angle θ is applied to a tool postpositioning instruction function generator 31 and a correction device 32so as to produce a corrected positioning instruction function Yi(t)which is supplied to a tool post positioning servo-system 27 for drivingthe tool drive unit (tool post) 16 in the direction of Y through controlamplifier 28, a servo-motor 17, and a gear box 29. A position detector30 is provided to detect the present Y axis position Yo(t) of the tooldrive unit 16 and the detected Y axis position Yo(t) is fed back to theinput of the control amplifier 28.

The delay in the tool post positioning servo-system 27 presents theproblem described above and the characteristic of this system isexpressed by a transfer function ^(K) L/S(1+TS) shown in a block shownin FIG. 4a, where Yi(s) represents the input instruction value, ε(s) thedeviation, Yo(s) the output, K_(L) the total gain of the servo-system,and T the time constant thereof. The transfer function is shown afterlaplace transformation. The total transfer function of the closed loopshown in FIG. 4a can be shown by

    1/(1+2ζToS+To.sup.2 S.sup.2)

as shown in FIG. 4b, where ζ and To are constants determined by the loopgain, and the moment of inertia of the load and the motor, and can bedetermined by K_(L) and T.

The tool post positioning instruction function generator 31 and thecorrection device 32 produce a corrected instruction value Yi(t) byadding the error ε(t) to the instruction value Y(t) for the purpose ofeliminating the error caused by the response delay of the servo-systemdescribed above. The tool post positioning instruction functiongenerator 31 produces the function Y(t) expressed by equation (1) inresponse to a signal representing the rotary angle and the correctiondevice 32 produces a signal representing the expected position errorquantity ε(t) in accordance with the value of the rotary angle θ. Assumenow that ω, R, E, L are constants as above described, the correctionfunction (position error quantity) ε(t) becomes a function of the rotaryangle θ so that the values of the function ε(t) corresponding todifferent values of θ are stored in a memory device 34 in the form ofprogrammable read only memory device, random access memory device or acore memory device and a correction signal ε(t) corresponding to thevalue of the rotary angle θ is read out by designating a read address ofthe memory device 34 corresponding to the value of θ applied to a readout control unit 33. The read out correction signal ε(t) is added to thepositioning instruction function Y(t) by an addition unit 35 to obtaincorrected instruction function Yi(t). Thus, the instruction functionYi(t) corresponds to the sum of the function Y(t) shown by equation (1)and the anticipated error quantity ε(t). In response to the deviationE_(b) (t) between the corrected instruction function Yi(t) and the fedback function Yo(t), the servo-system 27 drives the servo-motor 17. As aconsequence, the servo-system 27 responds to the corrected instructionfunction Yi(t) with a time delay but its response delay for the truepositioning instruction function Y(t) is much smaller and, accordingly,with a smaller error.

FIG. 5 shows a modification of the tool post positioning instructionfunction and the correction function generator 26 in which a computer 37is incorporated into the correction function generator 36 to receive thepositioning instruction function Y(t) generated by the tool postpositioning instruction function generator 31. The computer 37 processesin real time the input Y(t) by using a transfer function

    1/1+2ζToS+To.sup.2 S.sup.2

which is equivalent to that of the servo-system 27 to produce an outputYo(t) which is equivalent to a not corrected output of the servo-system27. Thus, the characteristic of the servo-system is simulated in realtime by the computer 37. The deviation between this output Yo(t) and theinput Y(t) is obtained by a subtractor 38 to produce an anticipatederror correction function ε(t). The function ε(t) thus obtained is addedto the positioning instruction function Y(t) by an adder 35 in the samemanner as above described. Thus, a corrected instruction function Yi(t)is obtained and applied to the servo-system 27.

In the correction device described above, the position error isdetermined beforehand and sent out in accordance with the rotary angle θfor correcting the instruction value but in the modified embodimentshown in FIG. 6, the instruction value Yi(t) and the feedback valueYo(t) from the servo-system are compared with each other intermittentlyfor calculating a phase delay ±ψ which is used to correct theinstruction value expressed by equation (1) thereby obtaining thecorrection value expressed by the following equation 2.

    Yi(t)=E.sub.cos (ωt±ψ)+√(R+L).sup.2 -E.sup.2 sin (ω±ψ)                                        (2)

In the embodiment shown in FIG. 6, intermittent angle values θn arespaced by a predetermined angle, for example 0°, 45°, 90° and 135°. Acoincidence circuit 101 is supplied with a value θ which shows therotary angle of the chuck 13 from the tool post positioning instructionfunction generator 31, and each time this value θ coincides with theintermittent angle value θn a coincidence signal CS is generated whichis applied to a correction discriminator 102. The correctiondiscriminator detects and discriminates the phase lag ±ψ of the positionfeedback value Yo(t) which is supplied from the tool post positioningservo system 27 and showing the present Y axis position of the tool post17 with respect to the output Yi(t) of the tool post positioninginstruction function generator 31 and when supplied with the coincidencesignal CS from the coincidence circuit 101, it detects the phase lag ±ψdepending upon the phase difference between Yi(t) and Yo(t). This phaselag ±ψ is applied to a correction calculator 103.

The correction calculator 103 corrects the output Y(t) of the tool postpositioning function generator 31 with the phase lag ±ψ detected by thecorrection discriminator 102. Thus, the correction calculator 103calculates the value Yi(t) expressed by equation 2 in accordance withthe phase lag ±ψ and applies the value Yi(t) to the tool postpositioning servo-system 27 as the instruction value.

As above described, the output of the tool positioning instructionfunction generator 31 is intermittently corrected each time the rotaryangle θ of the chuck 13 of the workpiece rotary shaft control unit 14coincides with a predetermined angle θn, so that the tool positioningservo-system 27 is controlled by the instruction value Y'i(t) which hasbeen corrected with phase delay ±ψ. Accordingly, although the toolpositioning servo-system 27 responds to the instruction value Y'i(t)with a time lag, it can respond to the true instruction value Yi(t)produced by the tool positioning instruction function generator 31 withan extremely small response delay.

The instruction function generator 31 may be of any desired type and acontrol instruction can be prepared very quickly when a functionequation is developed into Fourier's series and when respective Fouriercomponents are calcualted and then added together, which is advantageousfor the control.

Thus, by developing equation (1) into Fourier's series

    Y(t)=E cos ωt+(R+L) (a.sub.0 +a.sub.1 cos 2ωt+a.sub.2 cos 4ωt+a.sub.3 cos 6ωt . . . +A.sub.n cos 2nωt) (3)

where ##EQU1## Since L >> E, A^(n) →0. Since the Fourier's seriesconverges, it is possible to calculate the instruction value Yo(t) of apermissible accuracy by calculating up to a suitable n-th order.

FIG. 7 shows one example of a control instruction value generatingcircuit for performing the above described calculations which is usefulfor a machine tool which grinds the pin journals of the crankshaft of aninternal combustion engine shown in FIG. 1 and in which up to the 6thorder of the Fourier components of the function equation Y(t) expressedby equation (1) are calculated to form the control instruction valueY(t). Value E representing the rotary radius of the pin journal 11,value L representing the radius of tool 15 and value R representing theradius of the pin journal are applied to a calculator 120. Thecalculator 120 calculates values R+L and A=(E/R+L) from values E, L andR and applies values R+L and E to a calculator 121 and value A to athird calculator 122. Calculator 122 comprises a multiplier whichcalculates values A², A⁴ and A⁶ which are applied to a third calculator123 which calculates the coefficients a₀, a₁ . . . a_(n) shown inequations 4, 5, 6 and 7 from values A², A⁴ and A⁶ and applies thecalculated coefficients to fourth calculator 121.

The value ω representing the angular speed of the pin journal and acorrection value ψ are applied to a fifth calculator 124. The correctionvalue ψ is used to correct the time lag in the tool drive system 27 aswill be described later. The calculator 124 is also applied with a clockpulse C which is used to synchronize the workpiece drive shaft controlunit (FIG. 1) with the rotation of the pin journal 11. In response to ω,ψ and clock signal C, the calculator 124 calculates the values of(ωt+ψ), 2(ωt+ψ), 4(ωt+ψ) and 6(ωt+ψ) in synchronism with the rotation ofthe pin journal and these values are stored temporarily in registers 125through 128 respectively and then applied to a multiplexer 129 whichsequentially selects said values temporarily stored in respectiveregisters and applies them to a cosine function memory device 131through a gate circuit 130. The cosine function memory device 131comprises a read only memory device, for example, which is storing acorresponding cosine function value corresponding to an input address.Consequently, cosine functions cos (ωt+ψ), cos 2(ωt+ψ) cos 4(ωt+ψ) andcos 6(ωt+ψ) are sequentially read out from the cosine function memorydevice 131 corresponding to respective inputs (ωt+ψ), 2(ωt+ψ) 4(ωt+ψ)and 6(ωt+ψ) and these read out values are applied to a multiplexer 133through a read out register 132. The multiplexer 133 converts theseserially read out values into parallel values which are applied to thecalculator 121.

Calculator 121 produces signals (R+L) a₀, E cos (ωt+ψ), (R+L)a₁ cos2(ωt+ψ), (R+L) a₂ cos 4(ω+ψ), and (R+L) a₃ cos 6(ωt+ψ) respectivelyrepresenting the Fourier components of the Fourier's series shown inequation 3 based on values E, R+L which are supplied from calculator 20,values a₀, a₁, a₂ and a₃ which are supplied from calculator 23 andvalues cos (ωt+ψ), cos 2(ω+ψ), cos 4(ωt+ψ) and cos 6(ω+ψ) which aresupplied from the multiplexer 133. The outputs of the calculator 121 areadded together by an adder 134 to produce a value Yi(t)+E cos(ωt+ψ)+(R+L) a₀ +(R+L) a₁ cos 2(ω+ψ)+(R+L) a₂ cos 4(ω+ψ) +(R+L) a₃ cos6(ω+ ψ). This value is applied to the tool drive system 142 as thecontrol instruction value.

One of the outputs of the calculator 121, for example, the value (R+L)a₀ representing the DC term, is applied to adder 134 via an adder 135for the purpose of effecting a manual correction and an additioninstruction. In a state in which the addition instruction is not given,such instruction value that the tool will not come in contact with theworkpiece is given and, after obtaining information of actual movementsof the tool and workpiece, an additional instruction value is added tothe original instruction value for effecting cutting. By thisarrangement, a damage to the workpiece which may be caused by effectingcutting during a test driving can be avoided. A manual correction valueS₁ is applied to adder 135 while a preset addition instruction value S₂is applied to adder 135 through a gate circuit 136 opened by an additioninstruction signal OS. Where the manual correction is necessary, themanual correction value S₁ is added to the output of the calculator 21whereas when the addition instruction OS is applied, the gate circuit136 is opened to add the preset addition value S.sub. 2 to the output ofthe calculator 121.

As above described, a control instruction Yi(t) according to a functionequation Y(t) expressed by equation (1) is formed and applied to thetool drive system 142.

The embodiment shown in FIG. 7 operates as follows.

Let us assume that a correction value ψ'=0 is applied to calculator 124and that the control instruction value Yi(t) is calculated by the clocksignal C. The outer ωt of the calculator 124 is applied to thecoincidence circuit 104. This output ωt represents the rotary angle θ=ωtof the pin journal 11, and the coincidence circuit 104 is supplied withintermittent angle value θn (n=1, 2 . . . n which may be 0°, 45°, 90°,135°, 180°, for example). Each time signal ωt coincides with signal θn,the coincidence circuit 104 applies a coincidence signal to the register106. Since the register 106 is supplied with the output Yi(t) of theadder 134, the coincidence signal is given with a write timing. Moreparticularly, the register 106 is written with value Yi(t) each timevalue ωt coincides with the present angle θn. The values written intothe register 106 are applied to memory device 107 and sequentiallystored therein. In this manner, the value Yi(t) in one period is storedat each preset angle θn.

When the control instruction value Yi(t) is applied to the toolservo-system 27, it operates and a position feedback signal producedthereby is applied to the discriminator 105. The coincidence circuit 104produces a coincidence signal each time the value ωt produced by thecalculator 124 coincides with θn. This coincidence signal is applied tothe memory circuit 107 to read out a value Yi(t) corresponding to thevalue θn stored in the memory circuit 107 and the read out value Yi(t)is applied to a discriminator 105 through register 108. Thediscriminator 105 compares the phases of value Yi(t) and of the feedbackvalue Yo(t) to apply a value ψ' which represents the phase lag to thecalculator 124 as a correction value. Thus, the control instructionvalue Yi(t) is changed to Yi'(t) after correcting the phase angle toωt+ψ' thereby correcting the time lag tof the tool drive system 142.

In this embodiment, an approximate correction value ψ₀ of the phase lagof the tool drive system is preset in a calculator. Accordingly, theoutput of the discriminator 105 at this time is ψ'-ψ₀ which is a verysmall value.

What is claimed is:
 1. A numerical control system for controlling theposition of a machine tool with respect to a workpiece which is movingin a predetermined path, wherein the position of the workpiece iscontrolled by a control unit in response to a position instructioninput, said control unit including a position detector for determiningthe actual position of the workpiece, comprising:a generator forgenerating a control instruction signal which is a predeterminedfunction of the actual position of the workpiece; a servo-system forcontrolling the position of the machine tool, wherein said controlinstruction signal is the input to said servo-system; and a correctiondevice, for generating a correction signal and for changing the value ofthe control instruction signal in accordance with the correction signalto compensate for delay errors inherent in said servo-system.
 2. Thenumerical control system according to claim 1 wherein said correctiondevice includes an addder which adds said correction signal to saidcontrol instruction signal.
 3. The numerical control system according toclaim 1 wherein said correction device includes a memory device in whicha plurality of correction values are preset, and a read device forreading said memory device by utilizing predetermined positions of theworkpiece as the addresses of said memory device.
 4. The numericalcontrol system according to claim 1 wherein said correction deviceincludes a calculator, whose input is said control instruction signal,for effecting calculations corresponding to all transfer functions ofsaid servo-system, and means for substracting the output of saidcalculator from said control instruction signal to obtain the correctionsignal.
 5. The numerical control system according to claim 1 whereinsaid correction device includes a comparator which compares a feedbacksignal from the servo-system, said feedback signal corresponding to theposition of the machine tool, with said control instruction signal forproducing a signal representing the difference between the controlinstruction signal and the feedback signal, and an intermittentoperation device for intermittently operating said comparator device. 6.The numerical control system according to claim 5 wherein the workpieceis driven by a rotating reference shaft and wherein said intermittentoperation device comprises means for presetting at least onepredetermined angle of the reference shaft, and means for generating asignal which operates said comparator only when the rotary angle of saidreference shaft coincides with the present angle.
 7. The numericalcontrol system according to claim 1 wherein said generator comprisesmeans for decomposing a function equation into a plurality of Fouriercomponents and for independently calculating said components, and meansfor adding together said components.
 8. The numerical control systemaccording to claim 1 wherein said workpiece is a pin journal of acrankshaft, and said control instruction signal is expressed by thefollowing function equation:

    Y(t)=E cos ωt+√(R+L).sup.2 -E.sup.2 sin.sup.2 ωt,

where ω represents the angular velocity of said pin journal, L theradius of said tool, R the radius of said pin journal, and E thedistance between the center of said pin journal and the center ofrotation of said crankshaft.
 9. A numerical control system forcontrolling the position of a machine tool with respect to the side of acylindrical workpiece which is rotating eccentrically, comprising:aposition detector for determining the angular position of the workpiece;a generator connected to said position detector for generating a controlinstruction signal which is a predetermined function of the angularposition of the workpiece; a servo-system for controlling the positionof the machine tool in response to said control instruction signal; anda correction device, connected to the generator, for generating acorrection signal and changing the value of the control instructionsignal in order to compensate for time delay errors inherent in saidservo-system.